Question

The combined SAT scores for the students at a local high school are normally distributed with a mean of 1521 and a standard deviation of 298. The local college includes a minimum score of 1044 in its admission requirements. What percentage of students from this school earn scores that fail to satisfy the admission requirement?

Answer 1

Here random variable X is SAT scores for the students at a local high school

X follows normal with mean = and standard deviation =

Here we have to find P(X < 1044)

                                     where z is standard normal variable

                             = P(z < -1.6)                     (Round to 2 decimal)

                            = 0.0548                       (From statistical table of z values)

Percentage of students from high school earn scores that fail to satisfy the admission requirement

= 0.0548 * 100

= 5.48%

Percentage of students from high school earn scores that fail to satisfy the admission requirement is 5.48%